Shear Strain Localization in Plastic Deformations
Shear instabilities in the form of shear bands are often observed during high speed, plastic deformations of metals. According to one theory, their formation is attributed to effective strain-softening response, which results at high strain rates as the net outcome of the influence of thermal softening on the, normally, strain-hardening response of metals. In order to test the core instability mechanism set forth by such theories, we consider one-dimensional shear deformations of a material exhibiting strain softening and strain-rate sensitivity. The deformation is caused by either prescribed tractions or prescribed velocities. As it turns out, for moderate amounts of strain softening, strain-rate sensitivity exerts a dissipative effect and stabilizes the motion. However, once a threshold is exceeded, the response becomes unstable and shear strain localization can occur.
Unable to display preview. Download preview PDF.
- BPV] M. Bertsch, L. A. Peletier and S. M. Verduyn Lunel, The effect of temperature dependent viscosity on shear flow of incompressible fluids, SIAM J. Math. Anal, (to appear).Google Scholar
- [C]N. Charalambakis, Stabilite asymptotique lorsque t → ∞ en thermoviscoelasticité et ther- moplasticité, in “Nonlinear partial differential equations and their applications: Collège de France Seminar Vol IX”, (H. Brezis and J.-L. Lions, eds.), Pitman Res. Notes in Math. No 181, Longman Scientific and Technical, Essex, England, 1988.Google Scholar
- [D2]C. M. Dafermos, Contemporary Issues in the Dynamic Behavior of Continuous Media, LCDS Lecture Notes # 85–1, 1985.Google Scholar
- [L]T.-P. Liu, Nonlinear stability of shock waves for viscous conservation laws, Amer. Math. Soc. Mem. 328 (1985).Google Scholar
- [PW]M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1967.Google Scholar
- [T4]A. E. Tzavaras, Strain softening in viscoelasticity of the rate type, J. Integral Equations Appl. (to appear).Google Scholar